316 REPORT— 1901. 



as points or particles of perfectly regular (spherical) form, or at least 

 ignores their polarity if they have any, and, as a consequence of this 

 supposed regularity of the atoms, he attributes to some of Jordan's 

 systems an additional element of symmetry not necessarily involved by 

 their coincidence movements. Thus he regards some of the sixty-five 

 types as necessarily possessing planes of symmetry.' When, however, he 

 comes to speak of hemimorphous crystals, i.e., those which are differently 

 terminated at opposite ends of an axis of symmetry, he follows the 

 e.tample of Bravais — at least in his earlier writings — and resorts to the 

 supplementary hypothesis that the molecules possess polarity.^ 



The problem which 8ohncke sets himself to solve is, then, the con- 

 struction of all kinds of regular — i.e , homogeneously arranged ■* — assem- 

 blages composed of sets of identical particles, the shape of the particles 

 being ignored, or, in other words, treated as quite regular, i.e., spherical.'* 

 If he had succeeded in forming on these lines simple assemblages among 

 lohich were represented all the thirty-two classes of crystal symmetry, his 

 work would have been consistent with the supposition that crystals 

 consist in every case of a single kind of molecide whose shape and 

 constitution are destitute of polarity, the symmetry of the structure being 

 entirely determined by the relative situations of the molecules. He did 

 not, apparently, at any time hope to completely achieve this, for he 

 sdmitted the necessity of a supplementary hypothesis to account for 

 hemimorphism ; but, save for the few cases of this property, he appears, in 

 the first instance, to have hoped to reach an adequate theory based solely 

 on the relative jiosition of the molecules, without taking account of their 

 shape. 



The insufficiency of Sohncke's earlier theory that the molecules 

 are perfectly regular and all of one kind, and identically related to the 

 structure as a tvliole, was presently pointed out by several writers, among 

 whom may be mentioned Wulff'^ and Haag,'' the former in particular 

 having called attention to the existence of certain known crystal forms, 

 namely, those possessing the symmetry of the mineral dioptase, which 

 are not found represented among the sixty-five systems. 



Sohncke himself subsequently confessed the inadequacy of the theory 

 in question,' and was led to enlarge his method. Thus, after reviewing 

 some examples of more generalised point-systems devised by Wollaston, 

 Barlow, and Haag, he suggested the following modified theory : — 



Instead of regarding the spherical particles or points composing a 

 homogeneous assemblage as all of one kind, let a limited number of kinds 



■ Zeits. Kryst. Min., 1892, vol. xx. p. 448. 

 ^ Entmiclielung einer Theorie, etc., p. 200. 



' See Wiener's definition of homogeneity in Grundzilge der Weltordnnng, p. 82 

 et seq. Cf. Min. Ma//., 1896, vol. si. p. 120. 



* Comp. Ki-ystallsysteme und Krygtalhtructur, pp. Sg.'J, .'596, and p. G12. Sohncke 

 says {Zcitg. Kryst. Min., 18!)2, vol. xx. p. 452) : ' I have always considered the elemen- 

 tary particles to possess only .«o much symmetry that ihey donot disturb tlie .<-ymmetry 

 of the point-system.' The effect of this is that, so f.nr as the general symmetry is 

 concerned, they behave as though they were spherical. 



* 'Ueber die regelmiissigen Punktsysteme,' Zciis. Kryst. Min., 1888, vol. xiii. 

 pp. 503-5G6. 



' Die regularen ErystallMrjJer, Rothweil, 1887 (see reference in Zeits. Kryst. 

 Mill., 1888, vol. xvi. p. 501). 



' ' Bemerkungen zu Herrn Wulff's Theorie der Krystallstructur,' Zeits. Kryst. Mill., 

 vol. xiv. 417. See also ' Erweiterung der Theorie der Krystallstructur,' ii., p. 426, 



